A novel chaotic optimization algorithm and its applications

This paper presents a chaos-genetic algorithm (CGA) that combines chaos and genetic algorithms. It can be used to avoid trapping in local optima profiting from chaos'randomness,ergodicity and regularity. Its property of global asymptotical convergence has been proved with Markov chains in this paper. CGA was applied to the optimization of complex benchmark functions and artificial neural network's (ANN) training. In solving the complex benchmark functions,CGA needs less iterative number than GA and other chaotic optimization algorithms and always finds the optima of these functions. In training ANN,CGA uses less iterative number and shows strong generalization. It is proved that CGA is an efficient and convenient chaotic optimization algorithm.

CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

Background:To solve the cluster analysis better,we propose a new method based on the chaotic particle swarm optimization(CPSO)algorithm.Methods:In order to enhance the performance in clustering,we propose a novel method based on CPSO.We first evaluate the clustering performance of this model using the variance ratio criterion(VRC)as the evaluation metric.The effectiveness of the CPSO algorithm is compared with that of the traditional particle swarm optimization(PSO)algorithm.The CPSO aims to improve the VRC value while avoiding local optimal solutions.The simulated dataset is set at three levels of overlapping:non-overlapping,partial overlapping,and severe overlapping.Finally,we compare CPSO with two other methods.Results:By observing the comparative results,our proposed CPSO method performs outstandingly.In the conditions of non-overlapping,partial overlapping,and severe overlapping,our method has the best VRC values of 1683.2,620.5,and 275.6,respectively.The mean VRC values in these three cases are 1683.2,617.8,and 222.6.Conclusion:The CPSO performed better than other methods for cluster analysis problems.CPSO is effective for cluster analysis.

Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

Optimization of clay material mixture ratio and filling process in gypsum mine goaf

Because there is neither waste rock nor mill tailings in the gypsum mine, and the buildings on the goaf of gypsum mine are needed to be protected, the research proposed the scheme of the clay filling technology. Gypsum, cement, lime and water glass were used as adhesive, and the strength of different material ratios were investigated in this study. The influence factors of clay strength were obtained in the order of cement, gypsum, water glass and lime. The results show that the cement content is the determinant influence factor, and gypsum has positive effects, while the water glass can enhance both clay strength and the fluidity of the filing slurry. Furthermore, combining chaotic optimization method with neural network, the optimal ratio of composite cementing agent was obtained. The results show that the optimal ratio of water glass, cement, lime and clay (in quality) is 1.17:6.74:4.17:87.92 in the process of bottom self-flow filling, while the optimal ratio is 1.78:9.58:4.71:83.93 for roof-contacted filling. A novel filling process to fill in gypsum mine goaf with clay is established. The engineering practice shows that the filling cost is low, thus, notable economic benefit is achieved.

The measuring of spectral emissivity of object using chaotic optimal algorithm

There exist a considerable variety of factors affecting the spectral emissivity of an object. The authors have designed an improved combined neural network emissivity model, which can identify the continuous spectral emissivity and true temperature of any object only based on the measured brightness temperature data. In order to improve the accuracy of approximate calculations, the local minimum problem in the algorithm must be solved. Therefore, the authors design an optimal algorithm, i.e. a hybrid chaotic optimal algorithm, in which the chaos is used to roughly seek for the parameters involved in the model, and then a second seek for them is performed using the steepest descent. The modelling of emissivity settles the problems in assumptive models in multi-spectral theory.

A self-adaptive stochastic resonance system design and study in chaotic interference

The us of stochastic resonance （SR） can effectively achieve the detection of weak signal in white noise and colored noise. However, SR in chaotic interference is seldom involved. In view of the requirements for the detection of weak signal in the actual project and the relationship between the signal, chaotic interference, and nonlinear system in the bistable system, a self-adaptive SR system based on genetic algorithm is designed in this paper. It regards the output signal-to-noise ratio （SNR） as a fitness function and the system parameters are jointly encoded to gain optimal bistable system parameters, then the input signal is processed in the SR system with the optimal system parameters. Experimental results show that the system can keep the best state of SR under the condition of low input SNR, which ensures the effective detection and process of weak signal in low input SNR.

Short-Term Power Load Forecasting with Hybrid TPA-BiLSTM Prediction Model Based on CSSA

Since the existing prediction methods have encountered difficulties in processing themultiple influencing factors in short-term power load forecasting,we propose a bidirectional long short-term memory(BiLSTM)neural network model based on the temporal pattern attention(TPA)mechanism.Firstly,based on the grey relational analysis,datasets similar to forecast day are obtained.Secondly,thebidirectional LSTM layermodels the data of thehistorical load,temperature,humidity,and date-type and extracts complex relationships between data from the hidden row vectors obtained by the BiLSTM network,so that the influencing factors(with different characteristics)can select relevant information from different time steps to reduce the prediction error of the model.Simultaneously,the complex and nonlinear dependencies between time steps and sequences are extracted by the TPA mechanism,so the attention weight vector is constructed for the hidden layer output of BiLSTM and the relevant variables at different time steps are weighted to influence the input.Finally,the chaotic sparrow search algorithm(CSSA)is used to optimize the hyperparameter selection of the model.The short-term power load forecasting on different data sets shows that the average absolute errors of short-termpower load forecasting based on our method are 0.876 and 4.238,respectively,which is lower than other forecastingmethods,demonstrating the accuracy and stability of our model.

Time Delay Estimation in Radar System using Fuzzy Based Iterative Unscented Kalman Filter

RSs(Radar Systems)identify and trace targets and are commonly employed in applications like air traffic control and remote sensing.They are necessary for monitoring precise target trajectories.Estimations of RSs are non-linear as the parameters TDEs(time delay Estimations)and Doppler shifts are computed on receipt of echoes where EKFs(Extended Kalman Filters)and UKFs(Unscented Kalman Filters)have not been examined for computations.RSs,certain times result in poor accuracies and SNRs(low signal to noise ratios)especially,while encountering complicated environments.This work proposes IUKFs(Iterated UKFs)to track onlinefilter performances while using optimization techniques to enhance outcomes.The use of cost functions can assist state corrections while lowering costs.A new parameter is optimized using MCEHOs(Mutation Chaotic Elephant Herding Optimizations)by linearly approximating system non-linearity where OIUKFs(Optimized Iterative UKFs)predict a target's unknown parameters.To obtain optimal solutions theoretically,OIUKFs take less iteration,resulting in shorter execution times.The proposed OIUKFs provide numerical approximations which are derivative-free implementations.Simulation evaluation results with estimators show better performances in terms of reduced NMSEs(Normalized Mean Square Errors),RMSEs(Root Mean Squared Errors),SNRs,variances,and better accuracies than current approaches.

Stability analysis of slopes of expansive soils considering rainfall effect

Typical failure types of slopes of expansive soils are divided to two kinds： slip in surface layer and slip in shallow layer. Based on total strength law of expansive soils, the relationship between its water content and shear strength inculding cohesion and friction angle, was studied in detail. Acoording to change of water content and depth effect during rainfall, distribution of shear strength in slopes of expansive soils was analyzed. Finally, with a slope of expansive soils in Nanning city of Guangxi Autonomous Region of China as a case, safety factor and slip surface was studied.

Multi-UAV coordination control by chaotic grey wolf optimization based distributed MPC with event-triggered strategy

The paper proposes a new swarm intelligence-based distributed Model Predictive Control(MPC)approach for coordination control of multiple Unmanned Aerial Vehicles(UAVs).First,a distributed MPC framework is designed and each member only shares the information with neighbors.The Chaotic Grey Wolf Optimization(CGWO)method is developed on the basis of chaotic initialization and chaotic search to solve the local Finite Horizon Optimal Control Problem(FHOCP).Then,the distributed cost function is designed and integrated into each FHOCP to achieve multi-UAV formation control and trajectory tracking with no-fly zone constraint.Further,an event-triggered strategy is proposed to reduce the computational burden for the distributed MPC approach,which considers the predicted state errors and the convergence of cost function.Simulation results show that the CGWO-based distributed MPC approach is more computationally efficient to achieve multi-UAV coordination control than traditional method.

A GPS/BDS dual-mode positioning algorithm for a train based on CIPSO_EKF

When using global positioning system/BeiDou navigation satellite(GPS/BDS)dual-mode navigation system to locate a train,Kalman filter that is used to calculate train position has to be adjusted according to the features of the dual-mode observation.Due to multipath effect,positioning accuracy of present Kalman filter algorithm is really low.To solve this problem,a chaotic immune-vaccine particle swarm optimization_extended Kalman filter(CIPSO_EKF)algorithm is proposed to improve the output accuracy of the Kalman filter.By chaotic mapping and immunization,the particle swarm algorithm is first optimized,and then the optimized particle swarm algorithm is used to optimize the observation error covariance matrix.The optimal parameters are provided to the EKF,which can effectively reduce the impact of the observation value oscillation caused by multipath effect on positioning accuracy.At the same time,the train positioning results of EKF and CIPSO_EKF algorithms are compared.The eastward position errors and velocity errors show that CIPSO_EKF algorithm has faster convergence speed and higher real-time performance,which can effectively suppress interference and improve positioning accuracy.

Optimal Operation of Energy Internet Based on User Electricity Anxiety and Chaotic Spatial Variation Particle Swarm Optimization

Ignoring load characteristics and not considering user feeling with regard to the optimal operation of Energy Internet（EI） results in a large error in optimization. Thus, results are not consistent with the actual operating conditions. To solve these problems, this paper proposes an optimization method based on user Electricity Anxiety（EA） and Chaotic Space Variation Particle Swarm Optimization（CSVPSO）. First, the load is divided into critical load, translation load, shiftable load, and temperature load. Then, on the basis of the different load characteristics,the concept of the user EA degree is presented, and the optimization model of the EI is provided. This paper also presents a CSVPSO algorithm to solve the optimization problem because the traditional particle swarm optimization algorithm takes a long time and particles easily fall into the local optimum. In CSVPSO, the particles with lower fitness value are operated by using cross operation, and velocity variation is performed for particles with a speed lower than the setting threshold. The effectiveness of the proposed method is verified by simulation analysis.Simulation results show that the proposed method can be used to optimize the operation of EI on the basis of the full consideration of the load characteristics. Moreover, the optimization algorithm has high accuracy and computational efficiency.

Cuckoo Optimized Convolution Support Vector Machine for Big Health Data Processing

Big health data collection and storing for further analysis is a challenging task because this knowledge is big and has many features.Several cloud-based IoT health providers have been described in the literature previously.Furthermore,there are a number of issues related to time consumed and overall network performance when it comes to big data information.In the existing method,less performed optimization algorithms were used for optimizing the data.In the proposed method,the Chaotic Cuckoo Optimization algorithm was used for feature selection,and Convolutional Support Vector Machine(CSVM)was used.The research presents a method for analyzing healthcare information that uses in future prediction.The major goal is to take a variety of data while improving efficiency and minimizing process time.The suggested method employs a hybrid method that is divided into two stages.In the first stage,it reduces the features by using the Chaotic Cuckoo Optimization algorithm with Levy flight,opposition-based learning,and distributor operator.In the second stage,CSVM is used which combines the benefits of convolutional neural network(CNN)and SVM.The CSVM modifies CNN’s convolution product to learn hidden deep inside data sources.For improved economic flexibility,greater protection,greater analytics with confidentiality,and lower operating cost,the suggested approach is built on fog computing.Overall results of the experiments show that the suggested method can minimize the number of features in the datasets,enhances the accuracy by 82%,and decrease the time of the process.

Calculation of Available Transfer Capability Using Hybrid Chaotic Selfish Herd Optimizer and 24 Hours RES-thermal Scheduling

As fossil fuel stocks are being depleted,alternative sources of energy must be explored.Consequently,traditional thermal power plants must coexist with renewable resources,such as wind,solar,and hydro units,and all-day planning and operation techniques are necessary to safeguard nature while meeting the current demand.The fundamental components of contemporary power systems are the simultaneous decrease in generation costs and increase in the available transfer capacity(ATC)of current systems.Thermal units are linked to sources of renewable energy such as hydro,wind,and solar power,and are set up to run for 24 h.By contrast,new research reports that various chaotic maps are merged with various existing optimization methodologies to obtain better results than those without the inclusion of chaos.Chaos seems to increase the performance and convergence properties of existing optimization approaches.In this study,selfish animal tendencies,mathematically represented as selfish herd optimizers,were hybridized with chaotic phenomena and used to improve ATC and/or reduce generation costs,creating a multi-objective optimization problem.To evaluate the performance of the proposed hybridized optimization technique,an optimal power flow-based ATC was enforced under various hydro-thermal-solar-wind conditions,that is,the renewable energy source-thermal scheduling concept,on IEEE 9-bus,IEEE 39-bus,and Indian Northern Region Power Grid 246-bus test systems.The findings show that the proposed technique outperforms existing well-established optimization strategies.

Recognition of motor imagery tasks for BCI using CSP and chaotic PSO twin SVM

Accurate modeling and recognition of the brain activity patterns for reliable communication and interaction are still a challenging task for the motor imagery （MI） brain-computer interface （BCI） system. In this paper, we propose a common spatial pattern （CSP） and chaotic particle swarm optimization （CPSO） twin support vector machine （TWSVM） scheme for classification of MI electroencephalography （EEG）. The self-adaptive artifact removal and CSP were used to obtain the most distinguishable features. To improve the recognition results, CPSO was employed to tune the hyper-parameters of the TWSVM classifier. The usefulness of the proposed method was evaluated using the BCI competition IV-IIa dataset. The experimental results showed that the mean recognition accuracy of our proposed method was increased by 5.35%, 4.33%, 0.78%, 1.45%, and 9.26% compared with the CPSO support vector machine （SVM）, particle swarm optimization （PSO） TWSVM, linear discriminant analysis （LDA）, back propagation （BP） and probabilistic neural network （PNN）, respectively. Furthermore, it achieved a faster or comparable central processing unit （CPU） running time over the traditional SVM methods.

Fuzzy energy management strategy for parallel HEV based on pigeon-inspired optimization algorithm

Improvements in fuel consumption and emissions of hybrid electric vehicle(HEV)heavily depend upon an efficient energy management strategy(EMS).This paper presents an optimizing fuzzy control strategy of parallel hybrid electric vehicle em-

Improved deep mixed kernel randomized network for wind speed prediction

Forecasting wind speed is an extremely complicated and challenging problem due to its chaotic nature and its dependence on several atmospheric conditions.Although there are several intelligent techniques in the literature for wind speed prediction,their accuracies are not yet very reliable.Therefore,in this paper,a new hybrid intelligent technique named the deep mixed kernel random vector functional-link network auto-encoder(AE)is proposed for wind speed prediction.The proposed method eliminates manual tuning of hidden nodes with random weights and biases,providing prediction model generalization and representation learning.This reduces reconstruction error due to the exact inversion of the kernel matrix,unlike the pseudo-inverse in a random vector functional-link network,and short-ens the execution time.Furthermore,the presence of a direct link from the input to the output reduces the complexity of the prediction model and improves the prediction accuracy.The kernel parameters and coefficients of the mixed kernel system are optimized using a new chaotic sine–cosine Levy flight optimization technique.The lowest errors in terms of mean absolute error(0.4139),mean absolute percentage error(4.0081),root mean square error(0.4843),standard deviation error(1.1431)and index of agreement(0.9733)prove the efficiency of the proposed model in comparison with other deep learning models such as deep AEs,deep kernel extreme learning ma-chine AEs,deep kernel random vector functional-link network AEs,benchmark models such as least square support vector machine,autoregressive integrated moving average,extreme learning machines and their hybrid models along with different state-of-the-art methods.

Near Optimal PID Controllers for the Biped Robot While Walking on Uneven Terrains

The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation （PID） controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization （MCIWO） and particle swarm optimization （PSO） algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.

Comparative study of swarm intelligence-based saliency computation

Purpose–The purpose of this paper is to propose a new algorithm chaotic pigeon-inspired optimization(CPIO),which can effectively improve the computing efficiency of the basic Itti’s model for saliency-based detection.The CPIO algorithm and relevant applications are aimed at air surveillance for target detection.Design/methodology/approach–To compare the improvements of the performance on Itti’s model,three bio-inspired algorithms including particle swarm optimization(PSO),brain storm optimization(BSO)and CPIO are applied to optimize the weight coefficients of each feature map in the saliency computation.Findings–According to the experimental results in optimized Itti’s model,CPIO outperforms PSO in terms of computing efficiency and is superior to BSO in terms of searching ability.Therefore,CPIO provides the best overall properties among the three algorithms.Practical implications–The algorithm proposed in this paper can be extensively applied for fast,accurate and multi-target detections in aerial images.Originality/value–CPIO algorithm is originally proposed,which is very promising in solving complicated optimization problems.

Neuro-optimized numerical treatment of HIV infection model

In this paper,a neuro-optimized numerical method is presented for approximation of HIV virus progression model in the human body.The model is composed of coupled nonlinear system of differential equations(DEs)containing healthy and infected T-Cells and HIV free virus particles.The coupled system is transformed into feedforward artificial neural network(ANN)with Mexican hat wavelet function in the hidden layers.Two meta-heuristic algorithms based on chaotic particle swarm optimization(CPSO)and its hybrid version with local search technique are exploited to tune the parameters of ANN in an unsupervised manner of error function.A comprehensive testbed is established to observe the virus growth per day with performance metric containing fitness value,computational time complexity and convergence.The proposed solutions are compared with state of art Runge-Kutta method and Legendre Wavelet Collocation Method(LWCM).The core advantages of the proposed scheme are getting the solution on continuous grid,consistent convergence,simplicity in implementation and handling strong nonlinearity effectively.